Question

CSATHardPrelims 2020Reasoning

In the particular year 12th January is a Sunday, then which one of the following is correct?

Explanation

We are given that 12th January is a Sunday. We need to determine the correct statement regarding 12th or 15th July in both leap and non-leap years.

Counting the number of odd days from January to July We count the odd days from 12th January to 12th July separately for both leap and non-leap years.

Case 1: If the year is a leap year

January (after 12th) → 19 days → $(19 \mod 7) = 5$ odd days
February → 29 days → $(29 \mod 7) = 1$ odd day
March → 31 days → $(31 \mod 7) = 3$ odd days
April → 30 days → $(30 \mod 7) = 2$ odd days
May → 31 days → $(31 \mod 7) = 3$ odd days
June → 30 days → $(30 \mod 7) = 2$ odd days
12 days of July → $(12 \mod 7) = 5$ odd days Total odd days = $5 + 1 + 3 + 2 + 3 + 2 + 5 = 21$ odd days → $(21 \mod 7) = 0$ odd days

Since 12th January was Sunday, 12th July is also Sunday in a leap year.

Case 2: If the year is a non-leap year

January (after 12th) → 19 days → 5 odd days
February → 28 days → 0 odd days
March → 31 days → 3 odd days
April → 30 days → 2 odd days
May → 31 days → 3 odd days
June → 30 days → 2 odd days
12 days of July → 5 odd days Total odd days = $5 + 0 + 3 + 2 + 3 + 2 + 5 = 20$ odd days → $(20 \mod 7) = 6$ odd days